Function of Prosthetic Feet
Minimizing the weight of the prosthetic limb is very important for the amputee. The comfort and functionality of the prosthetic limb are highly dependent on its weight. This includes reducing the weight of the socket which attaches to the residual limb, and to the various connectors and struts comprising the total prosthetic limb. The most important areas where weight should be reduced are those on the distal portion of the prosthetic limb, i.e. the foot itself.
It is also very important that prosthetic feet do not fail in service to prevent injury and inconvenience to the amputee. Also, the prosthetist, who has a strong influence on a patient's foot choice, incurs cost to replace the failed foot. Prosthetic feet utilizing mechanical elements, i.e. pivot joints etc., have a markedly higher rate of in service failure than feet without such complicating design features. This has been an additional advantage of the carbon fiber prosthetic feet currently available.
Nature of Composite Materials
Composite materials, such as carbon-fiber/epoxy, provide a higher material stiffness and strength for a given weight than traditional materials. Consequently, these materials have found wide use in prosthetic feet.
High performance composite materials combine two or more materials with different mechanical characteristics. Taken separately, these constituent materials may not have the necessary properties for high strength structural applications. However, in combination, the resultant composite material can be a high performance structural material.
Carbon-fiber/epoxy illustrates this phenomenon. Epoxy resin is a relatively weak material with a relatively low stiffness. It has a tensile strength of roughly 10 Ksi. and a tensile modulus of roughly 750 Ksi. Its stress strain behavior is also nonlinear, showing a marked decrease in shear and tensile stiffness at higher elongations. For comparison, high strength steel has a tensile strength of approximately 100 Ksi. and a modulus of 30 Msi.
In contrast, carbon fiber has a very high tensile strength and stiffness in the fiber direction. It typically has a tensile strength of roughly 700 Ksi. and a very linear tensile modulus of roughly 33 Msi. That makes the fiber about 70 times stronger, and 50 times stiffer than the epoxy matrix material. However, the carbon fiber alone is not particularly useful as a structural material. It consists of a multitude of essentially continuous, very small fibers with virtually no compression strength, no shear strength, nor any mechanical properties transverse to the fibers.
Carbon-fiber/epoxy combines the best aspects of the constituent materials. The epoxy resin serves to transfer shear between fibers, stabilizes the fibers to support compressive loads, and provide some strength in the direction perpendicular to the fibers. An exemplary resultant material in its unidirectional form has a modulus of about 21 Msi. and strength of about 300 Ksi. in the fiber direction, and a density roughly one fifth that of steel. Composites allow the manufacture of prosthetic feet which are much lighter weight, and have higher energy storage capacities than what can be obtained using traditional metal structures alone.
Limitations of Composite Materials in Transverse Direction
Just as the advantages of fiber reinforced plastic materials are utilized when designing new prosthetic feet, the material's limitations must also be taken into consideration. These are material limitations that would not impact the design of traditional metal structures for example
Composite materials' primary limitation is its lack of material strength in directions that fibers are not oriented with. For example, for carbon-fiber/epoxy, in spite of the very high strengths in the fiber direction, its strength transverse to the fibers is only about 10 Ksi., basically the same as the unreinforced epoxy. A secondary limitation relates to the relative difficulty of fabricating complex shapes. Reference is now made to FIG. 17. which is a schematic of a laminate with partially cut away 174 to illustrate the different plies of the laminate. Arrows 171 and 172 indicate the in-plane directions. Arrow 170 indicates the out-of-plane direction. The present invention was developed to address both of these problems, which to date have not been addressed by composite prosthetic feet.
The reinforcing fibers provide the vast majority of load carrying capability in the composite. Consequently, composite structures are relatively weak and flexible when loaded in directions without fibers oriented in those directions. High performance composite structures need to have fibers aligned in every highly loaded direction to produce a structure with optimal efficiency.
Planar Nature of Composite Materials
Another characteristic of high performance composite structures is that they are usually planar in nature. One reason for this is the form of the raw material.
Perhaps the most common form of the raw material is unidirectional “prepreg”. In this form, a semisolid epoxy resin is preimpregnated into a thin sheet of fibers all aligned in a single direction. A cut away view of a typical laminate 173 is shown FIG. 17. The individual plies arranged in different orientations are denoted by 174, 175, and 176. Using this type of resin, a partially cured tacky semisolid material at room temperature, produces a sheet of handlable coherent material.
Another very common form of the raw material can be produced by first weaving fiber bundles into a flat cloth prior to being preimpregnated. Therefore the most common forms of the raw material are supplied as essentially very thin planar materials. These sheets or layers of material are laid upon each other at distinct orientations depending on the anticipated loads in those directions. These directions are restricted to being in the plane of the laminate, 171 and 172 in FIG. 17. This “layup” then forms a laminate with relatively high structural performance in-the-plane of the laminate. This belies the importance of the terms, “in-plane” 171, 172 or “out-of-plane” 170, commonly used in the composites industry.
The simplest composite structures to fabricate are flat or curved in only one direction. It is much simpler to assemble the planar raw material in shapes with curvature in only one direction, or with only a slight curvature in the opposite direction.
It is far more difficult to manufacture composite laminates/components having complex geometric shapes. That includes laminates which have a high degree of curvature in two orthogonal directions, i.e. compound curvature. Complex shaped composites structures are therefore less common than structures with laminates curved in primarily in one direction.
However, the structures containing laminates with a high degree of compound curvatures, i.e. more complex geometric shapes, have the potential to be far stronger and more efficient than the simpler geometries. These structures can be designed to allow the fibers to be aligned in all the load directions, rather than relying on the relatively week epoxy resin to carry the load.
Current Leaf Spring Type Prosthetic Feet
Referring now to FIGS. 15, 19, 20, and 25-31; in the past, dynamic response feet have primarily used a Composite Leaf Spring construction to store and release energy during gait. Some of the most widely recognized commercial embodiments of dynamic response feet, shown in FIG. 29-31, include Flexfoot by Ossur, Springlite by Otto Bock, Seattle feet by Seattle Systems and Carbon Copy by Ohio Willow Wood. All of these feet have been successful commercially and widely distributed.
These leaf spring type prosthetic foot designs are archetypical of the current state of the art of technological development in prosthetic feet. The foot 150 shown in FIG. 15 illustrates the most common features of these type of feet. FIGS. 25-28 illustrate the wide range of prior art prosthetic foot designs using this design approach. As seen in FIGS. 29-31, many of these designs have been reduced to commercial products. They rely primarily on bending or flexural stresses to store energy. Nearly all these have an initial curvature in only the fore-aft directions, being essentially straight in the lateral direction. Energy is stored and released primarily through flexure of the leaf spring like components and the design is two dimensional in nature.
In general, these Composite Leaf Spring foot designs require that transverse shear loads in the foot be carried by the epoxy matrix in “out-of-plane” shear. In fact the transverse shear strength of the laminate will commonly be the limiting strength factor affecting the foot design. For this reason, manufacturers of the current leaf spring type feet will typically select a prepreg carbon fiber material with the highest transverse shear strength available (measured as short beam shear strength).
Typical Structural Stresses and Strains in Prosthetic Feet
In general there are four critical types of internal loads in composite prosthetic foot structures, including: bending loads, transverse shear loads, interlaminar tensile loads, and torsional loads.
Bending loads are quite common in many structures. They are easy to understand, because it is possible to have a structure in pure bending, having no other internal loading. Bending loads produce bending stresses in the structure. These are axial stresses that vary across a cross section of the structure.
In contrast transverse shear loads are more difficult to conceptualize. Internal transverse shear load always give to internal bending loads. The two types of internal loading are interdependent. The form of this relationship in a simple structure is defined by the engineering equation V=dM/dx, where M is the moment and V is transverse shear. Specifically, the transverse shear in a structural member is equal to the rate of change of the moment down the length of the member. Almost all structural loadings in the real world include transverse shear. Transverse loads produce shear stresses, in addition to creating internal bending moments.
The design limitations inherent in Composite Leaf Spring feet make them very susceptible to interlaminar tensile stresses which can easily exceed the strength of the relatively weak epoxy matrix material. These stresses would typically produce delaminations in curved laminate areas. These stresses are produced when an initially curved section in the foot is loaded so as to open or flatten or flatten the curve. Arrow 191 in FIG. 19 indicates the location of these tensile stresses during the heel strike portion of the gait which can cause delamination. Arrow 201 in FIG. 20 illustrates how this tensile stress switches to a compressive stress during the toe off portion of the gait cycle. This type of delamination failure in laminated composites does not occur in metal structures.
Torsion is twisting force, a bending force actually, but applied transverse to the primary axis of the structure. Torsional loading, denoted as T, produces a shear stress. A torsional shear stress is a shear stress that varies across the cross section of the structure in a fashion similar to the way a bending axial stress varies across a cross section. The tubulous composite member 181 shown in FIG. 18 illustrates how prosthetic feet of the present invention can efficiently store energy in torsional stresses through in-plane loading, as opposed to the flat laminate member 173 shown in FIG. 17 illustrating that current Leaf Spring type prosthetic feet which cannot store significant energies as torsional stresses because they produce out-of-plane stresses.
Structural Mechanics of Spring Design
The energy storage or dynamic response prosthetic feet owe a large part of their performance to their ability to store energy during one portion of the gait and release it during a subsequent portion of the gait cycle. In essence these prosthetic feet act like springs. The weight of these springs is dependent on the structural efficiency of their design and materials used.
The structural efficiency and mechanical characteristics of springs is a well understood part of engineering mechanics. In particular there are several rules of thumb that experienced spring design engineers know intuitively. One of these rules is that stressing the spring material more evenly or uniformly increases efficiency, i.e. remove the material which is stressed less and is therefore less efficient. Increasing the wire length (length of active spring material) of a spring can be used to reduce stresses, increase maximum deflection, increase energy storage capacity. Obtaining a more compliant spring without failing requires a longer wire length. The only way to get a longer wire length into the constrained space envelope of a prosthetic foot is to coil it.
Traditional Autoclave Manufacturing Technology
An autoclave manufacturing process is utilized on most current composite construction dynamic response prosthetic feet. This process uses a single sided tool to produce components which are generally planar in nature. The shapes are usually curved in only one primary direction. The autoclave process is expensive and slow and is unsuited for the manufacture of hollow shapes with a complex geometry.
The material near the mid-plane of this planar structure are relatively inefficient, contributing weight but not capable of storing significant flexural energy. Most dynamic response prosthetic feet today are of relatively simple construction, being essentially planar in direction. Such feet are generally store energy almost exclusively in flexure. Delamination failures occasionally occur in current dynamic response prosthetic foot designs when the structure is loaded in a way to incur interlaminar tensile stresses or when interlaminar shear stresses exceed the strength of the relatively weak matrix material, usually epoxy resin, such as when a curved section in the foot is loaded so as to open or flatten or flatten the curve.
Delamination occurs because there are no fibers oriented in the direction of the tensile or shear load. Current autoclave construction processes are not conducive to the construction of structures which can place fibers in the direction where these tensile or shear delamination type loads are transmitted.